1. Tangent Lines
Geometry 11-1

2. Review
Review

3. Match the figures and terms

4. Circle – The set of all points in a plane that are equidistant from a given point
Center – Equidistant point of a circle
Radius – Distance from the center of a circle to a point on the circle
Diameter – Distance from a point on the circle to another point on the circle through the center of the circle
Chord – Line segment with endpoints on the circle
Secant – Line that intersects the circle twice
Circle Vocabulary

5. Tangent – A line that intersects a circle in exactly one point
Concentric – Circles with a common center
Common Tangent – Line tangent to two circles
Tangent Circles – Circles that intersect in exactly one point
Interior of a circle – points inside a circle
Exterior of a circle – points outside a circle
Circle Vocabulary

6. Intercepted Arc
Arc within an angle
Arc Vocabulary

7. Tangent Vocabulary Externally Tangent Circles
Circles that share a point of tangency but do not share any interior points
Tangent Vocabulary

8. Tangent Vocabulary Internally Tangent Circles
Circles that share a point of tangency and interior points
Tangent Vocabulary

9. New Material
Tangent Properties

10. Supplies Needed
Compass
Ruler
Protractor
Tangent Properties

11. Investigation Using a compass or a calculator Create a large circle
Add a tangent to the circle
Add a radius from the point of tangency to the center of the circle
Measure the angle between the tangent line and the radius
Investigation

12. Did everyone measure 90 degrees?
Is the converse true?
Investigation

13. A tangent to a circle is perpendicular to a radius drawn to the point of tangency.
If a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.
If a
Tangent Theorem

14. Tangent Theorems

15. Investigation Construct a circle
Construct two tangent lines that cross
Label the points as shown R S T
Investigation

16. Investigation Compare line segments RS and ST
These line segments are called tangent segments R S T
Investigation

17. Tangent Segments Theorem
Tangent segments to a circle from a point outside the circle are congruent
Tangent Segments Theorem

18. Tangent Segments Theorem

19. Inscribed in – when all the vertices of a polygon lie on a circle
Circumscribed about – When each side of a polygon is tangent to the circle
The polygon is circumscribed about
The polygon is Inscribed In
Vocabulary

20. Practice Problems

21. Practice Problems

22. Practice Problems

23. Practice Problems

24. Practice Problems

37. Pages 586 – 589
10 – 17 all, 20, 22, 52
Homework